Primitive Pythagorean triples: Pandigital Areas

 

a \; = \; m^2 \; - \; n^2
b \; = \; 2 \, m \, n
c \; = \; m^2 \; + \; n^2

 
PPT PAN 1

 

Paul found all the 10-digit pandigital area PPT:

1458376920    {39760,   73359,   83441}
1476958230    {6660,   443531,   443581}
1498637250    {39699,   75500,   85301}
1547836290    {37765,   81972,   90253}
1567984320    {31360,   99999,   104801}
1895472306    {53204,   71253,   88925}

2038719564    {2536,   1607823,   1607825}
2341685970    {18981,   246740,   247469}
2396574180    {60489,   79240,   99689}
2536714890    {70965,   71492,   100733}
2586943170    {53452,   96795,   110573}
2639875140    {6415,   823032,   823057}
2765943180    {27391,   201960,   203809}
2875039416    {11376,   505457,   505585}

3017482596    {21663,   278584,   279425}
3018275694    {35604,   169547,   173245}
3027851946    {56763,   106684,   120845}
3254897016    {47376,   137407,   145345}
3265814970    {42660,   153109,   158941}
3628457910    {54908,   132165,   143117}
3865729140    {82088,   94185,   124937}
3967421580    {84328,   94095,   126353}

4570391826    {87444,   104533,   136285}
4936581720    {30672,   321895,   323353}

5196387240    {22241,   467280,   467809}
5371296840    {82615,   130032,   154057}
5610297834    {60043,   186876,   196285}
5643897210    {48635,   232092,   237133}
5724691830    {40508,   282645,   285533}
5742836190    {46085,   249228,   253453}
5920386714    {54027,   219164,   225725}
5938710624    {36544,   325017,   327065}

6412937580    {69721,   183960,   196729}

7196485230    {92660,   155331,   180869}
7230985146    {98437,   146916,   176845}
7892563140    {66215,   238392,   247417}
7928164530    {68211,   232460,   242261}
7936482510    {50580,   313819,   317869}

8107536294    {88803,   182596,   203045}
8234159076    {70967,   232056,   242665}
8751902634    {59076,   296293,   302125}

9027435816    {109143,   165424,   198185}
9165423870    {121509,   150860,   193709}
9304817256    {73296,   253897,   264265}
9314275860    {78761,   236520,   249289}
9647821350    {101700,   189731,   215269}
9826435710    {68085,   288652,   296573}
9854271630    {86995,   226548,   242677}

 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
This entry was posted in Number Puzzles and tagged , . Bookmark the permalink.

5 Responses to Primitive Pythagorean triples: Pandigital Areas

  1. paul says:

    Here are all the 10 digit pan digital area primitive Triangles, format is
    {a, b, c, area, perimeter}

    {2536,1607823,1607825,2038719564,3218184}
    {6415,823032,823057,2639875140,1652504}
    {6660,443531,443581,1476958230,893772}
    {11376,505457,505585,2875039416,1022418}
    {18981,246740,247469,2341685970,513190}
    {21663,278584,279425,3017482596,579672}
    {22241,467280,467809,5196387240,957330}
    {27391,201960,203809,2765943180,433160}
    {30672,321895,323353,4936581720,675920}
    {31360,99999,104801,1567984320,236160}
    {35604,169547,173245,3018275694,378396}
    {36544,325017,327065,5938710624,688626}
    {37765,81972,90253,1547836290,209990}
    {39699,75500,85301,1498637250,200500}
    {39760,73359,83441,1458376920,196560}
    {40508,282645,285533,5724691830,608686}
    {42660,153109,158941,3265814970,354710}
    {46085,249228,253453,5742836190,548766}
    {47376,137407,145345,3254897016,330128}
    {48635,232092,237133,5643897210,517860}
    {50580,313819,317869,7936482510,682268}
    {53204,71253,88925,1895472306,213382}
    {53452,96795,110573,2586943170,260820}
    {54027,219164,225725,5920386714,498916}
    {54908,132165,143117,3628457910,330190}
    {56763,106684,120845,3027851946,284292}
    {59076,296293,302125,8751902634,657494}
    {60043,186876,196285,5610297834,443204}
    {60489,79240,99689,2396574180,239418}
    {66215,238392,247417,7892563140,552024}
    {68085,288652,296573,9826435710,653310}
    {68211,232460,242261,7928164530,542932}
    {69721,183960,196729,6412937580,450410}
    {70965,71492,100733,2536714890,243190}
    {70967,232056,242665,8234159076,545688}
    {73296,253897,264265,9304817256,591458}
    {78761,236520,249289,9314275860,564570}
    {82088,94185,124937,3865729140,301210}
    {82615,130032,154057,5371296840,366704}
    {84328,94095,126353,3967421580,304776}
    {86995,226548,242677,9854271630,556220}
    {87444,104533,136285,4570391826,328262}
    {88803,182596,203045,8107536294,474444}
    {92660,155331,180869,7196485230,428860}
    {98437,146916,176845,7230985146,422198}
    {101700,189731,215269,9647821350,506700}
    {109143,165424,198185,9027435816,472752}
    {121509,150860,193709,9165423870,466078}

    Paul.

  2. paul says:

    Using the parametric version to find PT’s misses quite a lot, so I never use if I want to be certain I have them all below a certain say small leg size.

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